A strictly formal, set-theoretical treatment of classical first-order logic
is given. Since this is done with the goal of a concrete Mizar formalization of
basic results (Lindenbaum lemma; Henkin, satisfiability, completeness and
Lowenheim-Skolem theorems) in mind, it turns into a systematic pursue of
simplification: we give up the notions of free occurrence, of derivation tree,
and study what inference rules are strictly needed to prove the mentioned
results. Afterwards, we discuss details of the actual Mizar implementation, and
give general techniques developed therein.Comment: Ph.D. thesis, defended on January, 20th, 201